Docs title-bar width toggle: click sticks, icon never updates, and layout flashes on refresh

Bug: docs title-bar width toggle is broken

The expand/collapse button next to "Copy page" on docs pages (visible at ≥1535px viewport) has three issues:

1. Click works only once, then gets stuck. Starting collapsed, the first click expands the layout. Subsequent clicks do nothing. Same in reverse: starting expanded, the first click collapses but it can't be re-expanded.
2. Icon never updates. Even when the layout state changes (e.g., on first click), the icon stays as UnfoldHorizontal (arrows pointing outward). It never flips to FoldHorizontal.
3. Flash on every refresh. When the preference is set to "expanded", refreshing the page paints the constrained (narrow) layout first, then snaps to expanded after hydration.

Repro

1. Open any docs page at a viewport ≥1535px (e.g. https://tanstack.com/router/latest/docs/framework/react/overview)
2. Click the expand/collapse icon on the right of the title bar
3. Try clicking it again — nothing happens, and the icon hasn't changed
4. Refresh while in the expanded state — observe the brief narrow → expanded flash

Video

https://github.com/user-attachments/assets/5a9b6ad5-5ca9-48d6-ad61-7b3dfa990096

I have a working branch with this fix locally. Will open a PR shortly ...

Abra la página de docs reproducida en la URL proporcionada e inspeccione el control de expandir/contraer de la barra de título situado junto a “Copy page.” Verifique que el interruptor pueda cambiar de estado repetidamente, que el icono refleje cada estado y que una preferencia expandida no muestre brevemente el diseño restringido después de actualizar. En la issue no se menciona ningún archivo fuente ni ninguna ruta de prueba.